Electrical Indicating
Instruments: AC
ENE 240 Electrical and Electronic Measurement
December 11, 2007, Class 6 (2/2007)
Werapon Chiracharit, Ph.D., ENE, KMUTT
werapon.chi@kmutt.ac.th
1
Alternating Current
• Current flows one way, then the other way,
continually reversing direction.
• Voltage is continually changing between
positive (+) and negative (-).
• Main electricity in Thailand has a frequency of
50Hz
• Average value is zero.
2
1
Averaging Power for AC
• P = I2R is just an instantaneous power at time t.
• Mean power or the total energy converted in
one cycle is
P = 1/T ∫t=0→T P dt
= 1/T ∫t=0→T I2R dt
= R [ 1/T ∫t=0→T I2 dt ]
= R [ sqrt(1/T ∫t=0→T I2 dt) ]2
= R (Irms)2
3
RMS or Effective Value
for only sinusoidal wave,
Iroot-mean-square = sqrt( I2average )
= sqrt( 1/T ∫t=0→T I2 dt )
= sqrt( 1/T ∫t=0→T [ Ipeaksin(ωt) ]2 dt )
= sqrt( (Ipeak)2/T ∫t=0→T sin2(ωt) dt )
= sqrt( (Ipeak)2/2T ∫t=0→T 1-cos(2ωt) dt )
= sqrt( (Ipeak)2/2 )
= Ipeak / sqrt(2)
= 0.707 Ipeak
4
2
Positive Half-Cycle Averaging
for only sinusoidal wave,
Iroot-mean-square = 2/T ∫t=0→T/2 I dt
= 2/T ∫t=0→T/2 Ipeaksin(ωt) dt
= 2Ipeak/T ∫t=0→T/2 sin(ωt) dt
= 2Ipeak/T [ -cos(ωt) ]t=0→T/2
= 2Ipeak/T [ -cos(ωT/2) + cos(0) ]
= 2Ipeak/T [ -cos(π) + cos(0) ]
= 4Ipeak/T
= 2Ipeak / π
= 0.636 Ipeak
5
Form Factor
Form Factor = Valuerms / Valuepositive-half-cycle
• for sin, FF = (Ipeak/sqrt(2)) / (2Ipeak/π)
= π / 2sqrt(2)
= 1.11
6
3
for Sinusoidal Wave
•
•
•
•
•
Irms = 0.707 Ipeak
Vrms = 0.707 Vpeak
I+ half cycle = 0.636 Ipeak
V+ half cycle = 0.636 Vpeak
FF = 1.11
7
for Square Wave
•
•
•
•
•
Irms = Ipeak
Vrms = Vpeak
I+ half cycle = Ipeak
V+ half cycle = Vpeak
FF = 1
8
4
AC on Moving-Coil Meter
• Alternating current = alternating torque
• Very low frequency => alternating pointer
• Other frequencies => pointer is not moved.
9
AC/DC Converter
• Rectifier circuit with bridge diodes
• Current flows in one direction.
• Inertia of moving coil = average value
• R = Ammeter
A
10
5
AC Calibration
AC meter shows root-mean-square
values of sinusoidal wave by calibrating the
scale with
Irms = FF × I+ half cycle
= 1.11 × I+ half cycle
11
Error for Other-Form Wave
• If the input signal is not a sinusoidal wave
form
Error = (1.11 - FF) / FF
×100%
12
6
Full-Scale-Deflection for AC Meter
• Each points in transformer (tap)
13
AC Voltmeter
• Multiplier resistance connected in series to
the bridge.
Bridge
Rmultiplier
14
7
Sensitivity: AC Vs DC
• e.g. if the AC input is 10 Vrms
Vpeak = 1.414 × 10 V
= 14.14 V
Vavg = 0.636 × 14.14 V
=9V
15
• Sensitivity = VAC / VDC ×100%
= Vavg / Vrms ×100%
= 90%
Bridge
AC Input
10Vrms
R = 10kΩ
IFSD = 1mA
16
8